List

Scientists recently found a complete list of all worlds that existed before the first humans appeared on Earth. They want to collect some statistics from it, so they define when two names are similar.

Two names are called $x$-similar if their suffixes of length $x$ are equal and their prefixes of length $x$ are equal.

The prefix of length $x$ of a string is its first $x$ characters. The suffix of length $x$ is its last $x$ characters. Taking a prefix or suffix longer than the string is an invalid operation.

For every integer $x$ from 1 to the maximum length of a name in the list, find the number of pairs of names that are $x$-similar.

The first line contains one integer $n$ ($1 \le n \le 10^5$), the number of names. Each of the next $n$ lines contains one name. The total length of all names does not exceed $500\,000$. Every name consists of lowercase Latin letters and has non-zero length.

On the first line, print $m$, the length of the longest name. On the line for $x$ ($2 \le x \le m + 1$), print the number of pairs of names that are $(x-1)$-similar.